Eigen  3.2.93
Homogeneous.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_HOMOGENEOUS_H
11 #define EIGEN_HOMOGENEOUS_H
12 
13 namespace Eigen {
14 
30 namespace internal {
31 
32 template<typename MatrixType,int Direction>
33 struct traits<Homogeneous<MatrixType,Direction> >
34  : traits<MatrixType>
35 {
36  typedef typename traits<MatrixType>::StorageKind StorageKind;
37  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
38  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
39  enum {
40  RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
41  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
42  ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
43  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
44  RowsAtCompileTime = Direction==Vertical ? RowsPlusOne : MatrixType::RowsAtCompileTime,
45  ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
46  MaxRowsAtCompileTime = RowsAtCompileTime,
47  MaxColsAtCompileTime = ColsAtCompileTime,
48  TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
49  Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
50  : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
51  : TmpFlags
52  };
53 };
54 
55 template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
56 template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
57 
58 } // end namespace internal
59 
60 template<typename MatrixType,int _Direction> class Homogeneous
61  : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
62 {
63  public:
64 
65  typedef MatrixType NestedExpression;
66  enum { Direction = _Direction };
67 
68  typedef MatrixBase<Homogeneous> Base;
69  EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
70 
71  explicit inline Homogeneous(const MatrixType& matrix)
72  : m_matrix(matrix)
73  {}
74 
75  inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical ? 1 : 0); }
76  inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
77 
78  const NestedExpression& nestedExpression() const { return m_matrix; }
79 
80  template<typename Rhs>
81  inline const Product<Homogeneous,Rhs>
82  operator* (const MatrixBase<Rhs>& rhs) const
83  {
84  eigen_assert(int(Direction)==Horizontal);
85  return Product<Homogeneous,Rhs>(*this,rhs.derived());
86  }
87 
88  template<typename Lhs> friend
89  inline const Product<Lhs,Homogeneous>
90  operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
91  {
92  eigen_assert(int(Direction)==Vertical);
93  return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
94  }
95 
96  template<typename Scalar, int Dim, int Mode, int Options> friend
97  inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
98  operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
99  {
100  eigen_assert(int(Direction)==Vertical);
101  return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
102  }
103 
104  template<typename Func>
105  EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
106  redux(const Func& func) const
107  {
108  return func(m_matrix.redux(func), Scalar(1));
109  }
110 
111  protected:
112  typename MatrixType::Nested m_matrix;
113 };
114 
126 template<typename Derived>
127 inline typename MatrixBase<Derived>::HomogeneousReturnType
129 {
130  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
131  return HomogeneousReturnType(derived());
132 }
133 
142 template<typename ExpressionType, int Direction>
145 {
146  return HomogeneousReturnType(_expression());
147 }
148 
157 template<typename Derived>
158 inline const typename MatrixBase<Derived>::HNormalizedReturnType
160 {
161  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
162  return ConstStartMinusOne(derived(),0,0,
163  ColsAtCompileTime==1?size()-1:1,
164  ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
165 }
166 
175 template<typename ExpressionType, int Direction>
178 {
179  return HNormalized_Block(_expression(),0,0,
180  Direction==Vertical ? _expression().rows()-1 : _expression().rows(),
181  Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
183  Direction==Vertical ? HNormalized_SizeMinusOne : 1,
184  Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
185  (HNormalized_Factors(_expression(),
186  Direction==Vertical ? _expression().rows()-1:0,
187  Direction==Horizontal ? _expression().cols()-1:0,
188  Direction==Vertical ? 1 : _expression().rows(),
189  Direction==Horizontal ? 1 : _expression().cols()),
190  Direction==Vertical ? _expression().rows()-1 : 1,
191  Direction==Horizontal ? _expression().cols()-1 : 1));
192 }
193 
194 namespace internal {
195 
196 template<typename MatrixOrTransformType>
197 struct take_matrix_for_product
198 {
199  typedef MatrixOrTransformType type;
200  static const type& run(const type &x) { return x; }
201 };
202 
203 template<typename Scalar, int Dim, int Mode,int Options>
204 struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
205 {
206  typedef Transform<Scalar, Dim, Mode, Options> TransformType;
208  static type run (const TransformType& x) { return x.affine(); }
209 };
210 
211 template<typename Scalar, int Dim, int Options>
212 struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
213 {
214  typedef Transform<Scalar, Dim, Projective, Options> TransformType;
215  typedef typename TransformType::MatrixType type;
216  static const type& run (const TransformType& x) { return x.matrix(); }
217 };
218 
219 template<typename MatrixType,typename Lhs>
220 struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
221 {
222  typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
223  typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
224  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
225  typedef typename make_proper_matrix_type<
226  typename traits<MatrixTypeCleaned>::Scalar,
227  LhsMatrixTypeCleaned::RowsAtCompileTime,
228  MatrixTypeCleaned::ColsAtCompileTime,
229  MatrixTypeCleaned::PlainObject::Options,
230  LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
231  MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
232 };
233 
234 template<typename MatrixType,typename Lhs>
235 struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
236  : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
237 {
238  typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
239  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
240  typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
241  homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
242  : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
243  m_rhs(rhs)
244  {}
245 
246  inline Index rows() const { return m_lhs.rows(); }
247  inline Index cols() const { return m_rhs.cols(); }
248 
249  template<typename Dest> void evalTo(Dest& dst) const
250  {
251  // FIXME investigate how to allow lazy evaluation of this product when possible
252  dst = Block<const LhsMatrixTypeNested,
253  LhsMatrixTypeNested::RowsAtCompileTime,
254  LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
255  (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
256  dst += m_lhs.col(m_lhs.cols()-1).rowwise()
257  .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
258  }
259 
260  typename LhsMatrixTypeCleaned::Nested m_lhs;
261  typename MatrixType::Nested m_rhs;
262 };
263 
264 template<typename MatrixType,typename Rhs>
265 struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
266 {
267  typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
268  MatrixType::RowsAtCompileTime,
269  Rhs::ColsAtCompileTime,
270  MatrixType::PlainObject::Options,
271  MatrixType::MaxRowsAtCompileTime,
272  Rhs::MaxColsAtCompileTime>::type ReturnType;
273 };
274 
275 template<typename MatrixType,typename Rhs>
276 struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
277  : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
278 {
279  typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
280  homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
281  : m_lhs(lhs), m_rhs(rhs)
282  {}
283 
284  inline Index rows() const { return m_lhs.rows(); }
285  inline Index cols() const { return m_rhs.cols(); }
286 
287  template<typename Dest> void evalTo(Dest& dst) const
288  {
289  // FIXME investigate how to allow lazy evaluation of this product when possible
290  dst = m_lhs * Block<const RhsNested,
291  RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
292  RhsNested::ColsAtCompileTime>
293  (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
294  dst += m_rhs.row(m_rhs.rows()-1).colwise()
295  .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
296  }
297 
298  typename MatrixType::Nested m_lhs;
299  typename Rhs::Nested m_rhs;
300 };
301 
302 template<typename ArgType,int Direction>
303 struct evaluator_traits<Homogeneous<ArgType,Direction> >
304 {
305  typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
306  typedef HomogeneousShape Shape;
307 };
308 
309 template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
310 
311 
312 template<typename ArgType,int Direction>
313 struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
314  : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
315 {
316  typedef Homogeneous<ArgType,Direction> XprType;
317  typedef typename XprType::PlainObject PlainObject;
318  typedef evaluator<PlainObject> Base;
319 
320  explicit unary_evaluator(const XprType& op)
321  : Base(), m_temp(op)
322  {
323  ::new (static_cast<Base*>(this)) Base(m_temp);
324  }
325 
326 protected:
327  PlainObject m_temp;
328 };
329 
330 // dense = homogeneous
331 template< typename DstXprType, typename ArgType, typename Scalar>
332 struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
333 {
334  typedef Homogeneous<ArgType,Vertical> SrcXprType;
335  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
336  {
337  dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
338  dst.row(dst.rows()-1).setOnes();
339  }
340 };
341 
342 // dense = homogeneous
343 template< typename DstXprType, typename ArgType, typename Scalar>
344 struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
345 {
346  typedef Homogeneous<ArgType,Horizontal> SrcXprType;
347  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
348  {
349  dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
350  dst.col(dst.cols()-1).setOnes();
351  }
352 };
353 
354 template<typename LhsArg, typename Rhs, int ProductTag>
355 struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
356 {
357  template<typename Dest>
358  static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
359  {
360  homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
361  }
362 };
363 
364 template<typename Lhs,typename Rhs>
365 struct homogeneous_right_product_refactoring_helper
366 {
367  enum {
368  Dim = Lhs::ColsAtCompileTime,
369  Rows = Lhs::RowsAtCompileTime
370  };
371  typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
372  typedef typename remove_const<LinearBlockConst>::type LinearBlock;
373  typedef typename Rhs::ConstRowXpr ConstantColumn;
374  typedef Replicate<const ConstantColumn,Rows,1> ConstantBlock;
375  typedef Product<Lhs,LinearBlock,LazyProduct> LinearProduct;
376  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
377 };
378 
379 template<typename Lhs, typename Rhs, int ProductTag>
380 struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
381  : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
382 {
383  typedef Product<Lhs, Rhs, LazyProduct> XprType;
384  typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
385  typedef typename helper::ConstantBlock ConstantBlock;
386  typedef typename helper::Xpr RefactoredXpr;
387  typedef evaluator<RefactoredXpr> Base;
388 
389  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
390  : Base( xpr.lhs().nestedExpression() .lazyProduct( xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
391  + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
392  {}
393 };
394 
395 template<typename Lhs, typename RhsArg, int ProductTag>
396 struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
397 {
398  template<typename Dest>
399  static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
400  {
401  homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
402  }
403 };
404 
405 template<typename Lhs,typename Rhs>
406 struct homogeneous_left_product_refactoring_helper
407 {
408  enum {
409  Dim = Rhs::RowsAtCompileTime,
410  Cols = Rhs::ColsAtCompileTime
411  };
412  typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type LinearBlockConst;
413  typedef typename remove_const<LinearBlockConst>::type LinearBlock;
414  typedef typename Lhs::ConstColXpr ConstantColumn;
415  typedef Replicate<const ConstantColumn,1,Cols> ConstantBlock;
416  typedef Product<LinearBlock,Rhs,LazyProduct> LinearProduct;
417  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
418 };
419 
420 template<typename Lhs, typename Rhs, int ProductTag>
421 struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
422  : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
423 {
424  typedef Product<Lhs, Rhs, LazyProduct> XprType;
425  typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
426  typedef typename helper::ConstantBlock ConstantBlock;
427  typedef typename helper::Xpr RefactoredXpr;
428  typedef evaluator<RefactoredXpr> Base;
429 
430  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
431  : Base( xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
432  + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
433  {}
434 };
435 
436 template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
437 struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
438 {
439  typedef Transform<Scalar,Dim,Mode,Options> TransformType;
440  template<typename Dest>
441  static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
442  {
443  homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
444  }
445 };
446 
447 template<typename ExpressionType, int Side, bool Transposed>
448 struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
449  : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
450 {};
451 
452 } // end namespace internal
453 
454 } // end namespace Eigen
455 
456 #endif // EIGEN_HOMOGENEOUS_H
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:71
Definition: Constants.h:265
Eigen::Index Index
Definition: VectorwiseOp.h:162
Expression of the transpose of a matrix.
Definition: Transpose.h:52
const MatrixType & matrix() const
Definition: Transform.h:395
Namespace containing all symbols from the Eigen library.
Definition: Core:271
const unsigned int RowMajorBit
Definition: Constants.h:61
const HNormalizedReturnType hnormalized() const
Definition: Homogeneous.h:177
Generic expression where a coefficient-wise binary operator is applied to two expressions.
Definition: CwiseBinaryOp.h:77
const Product< MatrixDerived, PermutationDerived, AliasFreeProduct > operator*(const MatrixBase< MatrixDerived > &matrix, const PermutationBase< PermutationDerived > &permutation)
Definition: PermutationMatrix.h:543
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: XprHelper.h:35
Expression of the multiple replication of a matrix or vector.
Definition: Replicate.h:61
Definition: Constants.h:268
Definition: Eigen_Colamd.h:50
const HNormalizedReturnType hnormalized() const
Definition: Homogeneous.h:159
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
HomogeneousReturnType homogeneous() const
Definition: Homogeneous.h:144
const int Dynamic
Definition: Constants.h:21
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Represents an homogeneous transformation in a N dimensional space.
Definition: ForwardDeclarations.h:274
HomogeneousReturnType homogeneous() const
Definition: Homogeneous.h:128
Expression of one (or a set of) homogeneous vector(s)
Definition: ForwardDeclarations.h:278